A soccer player heads the ball and sends it flying vertically upwards at a speed of 18.0 m/s . How high above the players ' head does the ball travel ?

16.53 m

Explanation:

The following data were obtained from the question:

Initial velocity (u) = 18.0 m/s.

Final velocity (v) = 0 m/s

Acceleration due to gravity (g) = 9.8 m/s²

Maximum height (h) =.?

The maximum height reached by the ball can be obtained as follow:

v² = u² – 2gh (since the ball is going against gravity)

0² = 18² – (2 × 9.8 × h)

0 = 324 – 19.6h

Rearrange

19.6h = 324

Divide both side by 19.6

h = 324 / 19.6

h = 16.53 m

Therefore, the maximum height reached by the ball is 16.53 m

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.